✕
Find the best tutors and institutes for Class 11 Tuition
Find Best Class 11 Tuition
Q14.7:
The motion of a particle executing simple harmonic motion is described by the displacement function, $x(t) = A cos (\omega t + \phi)$. If the initial ($t = 0$) position of the particle is 1 cm and its initial velocity is $\omega$ cm/s, what are its amplitude and initial phase angle ? The angular frequency of the particle is $\pi s^{-1}$. If instead of the cosine function, we choose the sine function to describe the SHM : $x = B sin (\omega t + \alpha)$, what are the amplitude and initial phase of the particle with the above initial conditions.
Solution :
Step 1: Given Variables and Initial Conditions
The displacement function for the Simple Harmonic Motion (SHM) is given by:
$x(t) = A \cos(\omega t + \phi)$
Given parameters at $t = 0$:
- $x(0) = 1 \text{ cm}$
- $v(0) = \frac{dx}{dt}|_{t=0} = \omega \text{ cm/s}$
- $\omega = \pi \text{ rad/s}$
Step 2: Analysis of the Cosine Function Representation
At $t = 0$:
- $x(0) = A \cos(\phi) = 1$ --- (Equation 1)
- $v(t) = \frac{d}{dt}[A \cos(\omega t + \phi)] = -A\omega \sin(\omega t + \phi)$
- $v(0) = -A\omega \sin(\phi) = \omega \implies A \sin(\phi) = -1$ --- (Equation 2)
To find amplitude $A$, we square and add Equation 1 and Equation 2 [Per the Pythagorean identity $\sin^2\phi + \cos^2\phi = 1$]:
$A^2(\cos^2\phi + \sin^2\phi) = (1)^2 + (-1)^2$
$A^2 = 2 \implies A = \sqrt{2} \text{ cm}$
To find the phase angle $\phi$, we divide Equation 2 by Equation 1:
$\tan(\phi) = \frac{-1}{1} = -1$
Since $\cos(\phi) > 0$ and $\sin(\phi) < 0$, the angle $\phi$ lies in the fourth quadrant: $\phi = -\frac{\pi}{4} \text{ rad} = -45^\circ$.
Step 3: Analysis of the Sine Function Representation
The displacement function is given by $x(t) = B \sin(\omega t + \alpha)$.
At $t = 0$:
- $x(0) = B \sin(\alpha) = 1$ --- (Equation 3)
- $v(t) = \frac{d}{dt}[B \sin(\omega t + \alpha)] = B\omega \cos(\omega t + \alpha)$
- $v(0) = B\omega \cos(\alpha) = \omega \implies B \cos(\alpha) = 1$ --- (Equation 4)
Squaring and adding Equation 3 and Equation 4:
$B^2(\sin^2\alpha + \cos^2\alpha) = 1^2 + 1^2$
$B^2 = 2 \implies B = \sqrt{2} \text{ cm}$
Dividing Equation 3 by Equation 4:
$\tan(\alpha) = \frac{1}{1} = 1$
Since $\sin(\alpha) > 0$ and $\cos(\alpha) > 0$, the angle $\alpha$ lies in the first quadrant: $\alpha = \frac{\pi}{4} \text{ rad} = 45^\circ$.
Step 4: Visualizing the Phase Relationship
Summary Comparison Table
| Function | Amplitude | Initial Phase Angle |
|---|---|---|
| $A \cos(\omega t + \phi)$ | $\sqrt{2} \text{ cm}$ | $-\pi/4 \text{ rad}$ |
| $B \sin(\omega t + \alpha)$ | $\sqrt{2} \text{ cm}$ | $\pi/4 \text{ rad}$ |
Final Solution: For the cosine function, the amplitude is $\sqrt{2} \text{ cm}$ and the phase angle is $-\pi/4 \text{ rad}$. For the sine function, the amplitude is $\sqrt{2} \text{ cm}$ and the phase angle is $\pi/4 \text{ rad}$.
More Questions from Class 11 Physics Oscillations Exercises
- Q13.1 (a): Which of the following examples represent periodic motion? A swimmer completing one (return) trip from one bank of a river to the other and back.
- Q13.1 (b): Which of the following examples represent periodic motion? A freely suspended bar magnet displaced from its N-S direction and released.
- Q13.1 (c): Which of the following examples represent periodic motion? A hydrogen molecule rotating about its centre of mass.
- Q13.1 (d): Which of the following examples represent periodic motion? An arrow released from a bow.
- Q13.10 (a): Let us take the position of mass when the spring is unstreched as (x = 0), and the direction from left to right as the positive direction of (x)-axis. Give (x) as a function of time (t) for the oscillating mass if at the moment we start the stopwatch ((t = 0)), the mass is at the mean position. In what way do these functions for SHM differ from each other, in frequency, in amplitude or the initial phase?
- Q13.10 (b): Let us take the position of mass when the spring is unstreched as (x = 0), and the direction from left to right as the positive direction of (x)-axis. Give (x) as a function of time (t) for the oscillating mass if at the moment we start the stopwatch ((t = 0)), the mass is at the maximum stretched position. In what way do these functions for SHM differ from each other, in frequency, in amplitude or the initial phase?
- Q13.10 (c): Let us take the position of mass when the spring is unstreched as (x = 0), and the direction from left to right as the positive direction of (x)-axis. Give (x) as a function of time (t) for the oscillating mass if at the moment we start the stopwatch ((t = 0)), the mass is at the maximum compressed position. In what way do these functions for SHM differ from each other, in frequency, in amplitude or the initial phase?
- Q13.11: Figures 13.20 correspond to two circular motions. The radius of the circle, the period of revolution, the initial position, and the sense of revolution (i.e. clockwise or anti-clockwise) are indicated on each figure. Obtain the corresponding simple harmonic motions of the (x)-projection of the radius vector of the revolving particle P, in each case.
- Q13.12 (a): Plot the corresponding reference circle for each of the following simple harmonic motions. Indicate the initial ((t =0)) position of the particle, the radius of the circle, and the angular speed of the rotating particle. For simplicity, the sense of rotation may be fixed to be anticlockwise in every case: ((x) is in cm and (t) is in s). (x = -2 \sin (3t + \pi/3))
- Q13.12 (b): Plot the corresponding reference circle for each of the following simple harmonic motions. Indicate the initial ((t =0)) position of the particle, the radius of the circle, and the angular speed of the rotating particle. For simplicity, the sense of rotation may be fixed to be anticlockwise in every case: ((x) is in cm and (t) is in s). (x = \cos (\pi/6 - t))
- Q13.12 (c): Plot the corresponding reference circle for each of the following simple harmonic motions. Indicate the initial ((t =0)) position of the particle, the radius of the circle, and the angular speed of the rotating particle. For simplicity, the sense of rotation may be fixed to be anticlockwise in every case: ((x) is in cm and (t) is in s). (x = 3 \sin (2\pi t + \pi/4))
- Q13.12 (d): Plot the corresponding reference circle for each of the following simple harmonic motions. Indicate the initial ((t =0)) position of the particle, the radius of the circle, and the angular speed of the rotating particle. For simplicity, the sense of rotation may be fixed to be anticlockwise in every case: ((x) is in cm and (t) is in s). (x = 2 \cos \pi t)
- Q13.13 (a): Figure 13.21(a) shows a spring of force constant (k) clamped rigidly at one end and a mass (m) attached to its free end. A force (F) applied at the free end stretches the spring. Figure 13.21 (b) shows the same spring with both ends free and attached to a mass (m) at either end. Each end of the spring in Fig. 13.21(b) is stretched by the same force (F). What is the maximum extension of the spring in the two cases ?
- Q13.13 (b): Figure 13.21(a) shows a spring of force constant (k) clamped rigidly at one end and a mass (m) attached to its free end. A force (F) applied at the free end stretches the spring. Figure 13.21 (b) shows the same spring with both ends free and attached to a mass (m) at either end. Each end of the spring in Fig. 13.21(b) is stretched by the same force (F). If the mass in Fig. (a) and the two masses in Fig. (b) are released, what is the period of oscillation in each case ?
- Q13.14: The piston in the cylinder head of a locomotive has a stroke (twice the amplitude) of 1.0 m. If the piston moves with simple harmonic motion with an angular frequency of 200 rad/min, what is its maximum speed ?
- Q13.15: The acceleration due to gravity on the surface of moon is 1.7 m s\(^{-2}\). What is the time period of a simple pendulum on the surface of moon if its time period on the surface of earth is 3.5 s ? ((g) on the surface of earth is 9.8 m s\(^{-2}\))
- Q13.16: A simple pendulum of length (l) and having a bob of mass (M) is suspended in a car. The car is moving on a circular track of radius (R) with a uniform speed (v). If the pendulum makes small oscillations in a radial direction about its equilibrium position, what will be its time period ?
- Q13.17: A cylindrical piece of cork of density of base area (A) and height (h) floats in a liquid of density (\rho_{l}). The cork is depressed slightly and then released. Show that the cork oscillates up and down simple harmonically with a period (T = 2\pi \sqrt{\frac{h\rho}{\rho_{l}g}}) where (\rho) is the density of cork. (Ignore damping due to viscosity of the liquid).
- Q13.18: One end of a U-tube containing mercury is connected to a suction pump and the other end to atmosphere. A small pressure difference is maintained between the two columns. Show that, when the suction pump is removed, the column of mercury in the U-tube executes simple harmonic motion.
- Q13.2 (a): Which of the following examples represent (nearly) simple harmonic motion and which represent periodic but not simple harmonic motion? the rotation of earth about its axis.
- Q13.2 (b): Which of the following examples represent (nearly) simple harmonic motion and which represent periodic but not simple harmonic motion? motion of an oscillating mercury column in a U-tube.
- Q13.2 (c): Which of the following examples represent (nearly) simple harmonic motion and which represent periodic but not simple harmonic motion? motion of a ball bearing inside a smooth curved bowl, when released from a point slightly above the lower most point.
- Q13.2 (d): Which of the following examples represent (nearly) simple harmonic motion and which represent periodic but not simple harmonic motion? general vibrations of a polyatomic molecule about its equilibrium position.
- Q13.3: Below fig. depicts four (x-t) plots for linear motion of a particle. Which of the plots represent periodic motion? What is the period of motion (in case of periodic motion) ?
- Q13.4 (a): Which of the following functions of time represent (a) simple harmonic, (b) periodic but not simple harmonic, and (c) non-periodic motion? Give period for each case of periodic motion ((ω) is any positive constant): (\sin \omega t - \cos \omega t)
- Q13.4 (b): Which of the following functions of time represent (a) simple harmonic, (b) periodic but not simple harmonic, and (c) non-periodic motion? Give period for each case of periodic motion ((ω) is any positive constant): (\sin^{3} \omega t)
- Q13.4 (c): Which of the following functions of time represent (a) simple harmonic, (b) periodic but not simple harmonic, and (c) non-periodic motion? Give period for each case of periodic motion ((ω) is any positive constant): (3 \cos (\pi/4 - 2\omega t))
- Q13.4 (d): Which of the following functions of time represent (a) simple harmonic, (b) periodic but not simple harmonic, and (c) non-periodic motion? Give period for each case of periodic motion ((ω) is any positive constant): (\cos \omega t + \cos 3\omega t + \cos 5\omega t)
- Q13.4 (e): Which of the following functions of time represent (a) simple harmonic, (b) periodic but not simple harmonic, and (c) non-periodic motion? Give period for each case of periodic motion ((ω) is any positive constant): (\exp (-\omega^{2}t^{2}))
- Q13.4 (f): Which of the following functions of time represent (a) simple harmonic, (b) periodic but not simple harmonic, and (c) non-periodic motion? Give period for each case of periodic motion ((ω) is any positive constant): (1 + \omega t + \omega^{2}t^{2})
- Q13.5 (a): A particle is in linear simple harmonic motion between two points, A and B, 10 cm apart. Take the direction from A to B as the positive direction and give the signs of velocity, acceleration and force on the particle when it is at the end A,
- Q13.5 (b): A particle is in linear simple harmonic motion between two points, A and B, 10 cm apart. Take the direction from A to B as the positive direction and give the signs of velocity, acceleration and force on the particle when it is at the end B,
- Q13.5 (c): A particle is in linear simple harmonic motion between two points, A and B, 10 cm apart. Take the direction from A to B as the positive direction and give the signs of velocity, acceleration and force on the particle when it is at the mid-point of AB going towards A,
- Q13.5 (d): A particle is in linear simple harmonic motion between two points, A and B, 10 cm apart. Take the direction from A to B as the positive direction and give the signs of velocity, acceleration and force on the particle when it is at 2 cm away from B going towards A,
- Q13.5 (e): A particle is in linear simple harmonic motion between two points, A and B, 10 cm apart. Take the direction from A to B as the positive direction and give the signs of velocity, acceleration and force on the particle when it is at 3 cm away from A going towards B, and
- Q13.5 (f): A particle is in linear simple harmonic motion between two points, A and B, 10 cm apart. Take the direction from A to B as the positive direction and give the signs of velocity, acceleration and force on the particle when it is at 4 cm away from B going towards A.
- Q13.6 (a): Which of the following relationships between the acceleration (a) and the displacement (x) of a particle involve simple harmonic motion? (a = 0.7x)
- Q13.6 (b): Which of the following relationships between the acceleration (a) and the displacement (x) of a particle involve simple harmonic motion? (a = -200x^{2})
- Q13.6 (c): Which of the following relationships between the acceleration (a) and the displacement (x) of a particle involve simple harmonic motion? (a = -10x)
- Q13.6 (d): Which of the following relationships between the acceleration (a) and the displacement (x) of a particle involve simple harmonic motion? (a = 100x^{3})
- Q13.7: The motion of a particle executing simple harmonic motion is described by the displacement function, (x(t) = A \cos (\omega t + \phi)). If the initial ((t = 0)) position of the particle is 1 cm and its initial velocity is (\omega) cm/s, what are its amplitude and initial phase angle ? The angular frequency of the particle is (\pi \text{ s}^{-1}). If instead of the cosine function, we choose the sine function to describe the SHM : (x = B \sin (\omega t + \alpha)), what are the amplitude and initial phase of the particle with the above initial conditions.
- Q13.8: A spring balance has a scale that reads from 0 to 50 kg. The length of the scale is 20 cm. A body suspended from this balance, when displaced and released, oscillates with a period of 0.6 s. What is the weight of the body ?
- Q13.9 (i): A spring having with a spring constant 1200 N m\(^{-1}\) is mounted on a horizontal table as shown in Fig. 13.19. A mass of 3 kg is attached to the free end of the spring. The mass is then pulled sideways to a distance of 2.0 cm and released. Determine the frequency of oscillations,
- Q13.9 (ii): A spring having with a spring constant 1200 N m\(^{-1}\) is mounted on a horizontal table as shown in Fig. 13.19. A mass of 3 kg is attached to the free end of the spring. The mass is then pulled sideways to a distance of 2.0 cm and released. Determine maximum acceleration of the mass,
- Q13.9 (iii): A spring having with a spring constant 1200 N m\(^{-1}\) is mounted on a horizontal table as shown in Fig. 13.19. A mass of 3 kg is attached to the free end of the spring. The mass is then pulled sideways to a distance of 2.0 cm and released. Determine the maximum speed of the mass.
- Q14.1(a): Which of the following examples represent periodic motion? (a) A swimmer completing one (return) trip from one bank of a river to the other and back.
- Q14.1(b): Which of the following examples represent periodic motion? (b) A freely suspended bar magnet displaced from its N-S direction and released.
- Q14.1(c): Which of the following examples represent periodic motion? (c) A hydrogen molecule rotating about its centre of mass.
- Q14.1(d): Which of the following examples represent periodic motion? (d) An arrow released from a bow.
- Q14.10(a): Let us take the position of mass when the spring is unstreched as $x = 0$, and the direction from left to right as the positive direction of x-axis. Give $x$ as a function of time $t$ for the oscillating mass if at the moment we start the stopwatch ($t = 0$), the mass is (a) at the mean position,
- Q14.10(b): Let us take the position of mass when the spring is unstreched as $x = 0$, and the direction from left to right as the positive direction of x-axis. Give $x$ as a function of time $t$ for the oscillating mass if at the moment we start the stopwatch ($t = 0$), the mass is (b) at the maximum stretched position, and
- Q14.10(c): Let us take the position of mass when the spring is unstreched as $x = 0$, and the direction from left to right as the positive direction of x-axis. Give $x$ as a function of time $t$ for the oscillating mass if at the moment we start the stopwatch ($t = 0$), the mass is (c) at the maximum compressed position. In what way do these functions for SHM differ from each other, in frequency, in amplitude or the initial phase?
- Q14.11: Figures 14.25 correspond to two circular motions. The radius of the circle, the period of revolution, the initial position, and the sense of revolution (i.e. clockwise or anti-clockwise) are indicated on each figure. Obtain the corresponding simple harmonic motions of the x-projection of the radius vector of the revolving particle P, in each case.
- Q14.12(a): Plot the corresponding reference circle for each of the following simple harmonic motions. Indicate the initial ($t =0$) position of the particle, the radius of the circle, and the angular speed of the rotating particle. For simplicity, the sense of rotation may be fixed to be anticlockwise in every case: ($x$ is in cm and $t$ is in s). (a) $x = –2 sin (3t + \pi/3)$
- Q14.12(b): Plot the corresponding reference circle for each of the following simple harmonic motions. Indicate the initial ($t =0$) position of the particle, the radius of the circle, and the angular speed of the rotating particle. For simplicity, the sense of rotation may be fixed to be anticlockwise in every case: ($x$ is in cm and $t$ is in s). (b) $x = cos (\pi/6 – t)$
- Q14.12(c): Plot the corresponding reference circle for each of the following simple harmonic motions. Indicate the initial ($t =0$) position of the particle, the radius of the circle, and the angular speed of the rotating particle. For simplicity, the sense of rotation may be fixed to be anticlockwise in every case: ($x$ is in cm and $t$ is in s). (c) $x = 3 sin (2\pi t + \pi/4)$
- Q14.12(d): Plot the corresponding reference circle for each of the following simple harmonic motions. Indicate the initial ($t =0$) position of the particle, the radius of the circle, and the angular speed of the rotating particle. For simplicity, the sense of rotation may be fixed to be anticlockwise in every case: ($x$ is in cm and $t$ is in s). (d) $x = 2 cos \pi t$
- Q14.13(a): Figure 14.26 (a) shows a spring of force constant $k$ clamped rigidly at one end and a mass $m$ attached to its free end. A force $F$ applied at the free end stretches the spring. Figure 14.26 (b) shows the same spring with both ends free and attached to a mass $m$ at either end. Each end of the spring in Fig. 14.26(b) is stretched by the same force $F$. (a) What is the maximum extension of the spring in the two cases ?
- Q14.13(b): Figure 14.26 (a) shows a spring of force constant $k$ clamped rigidly at one end and a mass $m$ attached to its free end. A force $F$ applied at the free end stretches the spring. Figure 14.26 (b) shows the same spring with both ends free and attached to a mass $m$ at either end. Each end of the spring in Fig. 14.26(b) is stretched by the same force $F$. (b) If the mass in Fig. (a) and the two masses in Fig. (b) are released, what is the period of oscillation in each case ?
- Q14.14: The piston in the cylinder head of a locomotive has a stroke (twice the amplitude) of 1.0 m. If the piston moves with simple harmonic motion with an angular frequency of 200 rad/min, what is its maximum speed ?
- Q14.15: The acceleration due to gravity on the surface of moon is $1.7 m s^{-2}$. What is the time period of a simple pendulum on the surface of moon if its time period on the surface of earth is 3.5 s ? ($g$ on the surface of earth is $9.8 m s^{-2}$)
- Q14.16(a): Answer the following questions : (a) Time period of a particle in SHM depends on the force constant $k$ and mass $m$ of the particle: $T = 2\pi \sqrt{\frac{m}{k}}$. A simple pendulum executes SHM approximately. Why then is the time period of a pendulum independent of the mass of the pendulum?
- Q14.16(b): Answer the following questions : (b) The motion of a simple pendulum is approximately simple harmonic for small angle oscillations. For larger angles of oscillation, a more involved analysis shows that $T$ is greater than $2\pi \sqrt{\frac{l}{g}}$. Think of a qualitative argument to appreciate this result.
- Q14.16(c): Answer the following questions : (c) A man with a wristwatch on his hand falls from the top of a tower. Does the watch give correct time during the free fall ?
- Q14.16(d): Answer the following questions : (d) What is the frequency of oscillation of a simple pendulum mounted in a cabin that is freely falling under gravity ?
- Q14.17: A simple pendulum of length $l$ and having a bob of mass $M$ is suspended in a car. The car is moving on a circular track of radius $R$ with a uniform speed $v$. If the pendulum makes small oscillations in a radial direction about its equilibrium position, what will be its time period ?
- Q14.18: A cylindrical piece of cork of density of base area $A$ and height $h$ floats in a liquid of density $\rho_l$. The cork is depressed slightly and then released. Show that the cork oscillates up and down simple harmonically with a period $T = 2\pi \sqrt{\frac{h\rho}{g\rho_l}}$ where $\rho$ is the density of cork. (Ignore damping due to viscosity of the liquid).
- Q14.19: One end of a U-tube containing mercury is connected to a suction pump and the other end to atmosphere. A small pressure difference is maintained between the two columns. Show that, when the suction pump is removed, the column of mercury in the U-tube executes simple harmonic motion.
- Q14.2(a): Which of the following examples represent (nearly) simple harmonic motion and which represent periodic but not simple harmonic motion? (a) the rotation of earth about its axis.
- Q14.2(b): Which of the following examples represent (nearly) simple harmonic motion and which represent periodic but not simple harmonic motion? (b) motion of an oscillating mercury column in a U-tube.
- Q14.2(c): Which of the following examples represent (nearly) simple harmonic motion and which represent periodic but not simple harmonic motion? (c) motion of a ball bearing inside a smooth curved bowl, when released from a point slightly above the lower most point.
- Q14.2(d): Which of the following examples represent (nearly) simple harmonic motion and which represent periodic but not simple harmonic motion? (d) general vibrations of a polyatomic molecule about its equilibrium position.
- Q14.3: Fig. 14.23 depicts four x-t plots for linear motion of a particle. Which of the plots represent periodic motion? What is the period of motion (in case of periodic motion) ?
- Q14.4(a): Which of the following functions of time represent (a) simple harmonic, (b) periodic but not simple harmonic, and (c) non-periodic motion? Give period for each case of periodic motion ($\omega$ is any positive constant): (a) $sin \omega t – cos \omega t$
- Q14.4(b): Which of the following functions of time represent (a) simple harmonic, (b) periodic but not simple harmonic, and (c) non-periodic motion? Give period for each case of periodic motion ($\omega$ is any positive constant): (b) $sin^3 \omega t$
- Q14.4(c): Which of the following functions of time represent (a) simple harmonic, (b) periodic but not simple harmonic, and (c) non-periodic motion? Give period for each case of periodic motion ($\omega$ is any positive constant): (c) $3 cos (\frac{\pi}{4} – 2\omega t)$
- Q14.4(d): Which of the following functions of time represent (a) simple harmonic, (b) periodic but not simple harmonic, and (c) non-periodic motion? Give period for each case of periodic motion ($\omega$ is any positive constant): (d) $cos \omega t + cos 3\omega t + cos 5\omega t$
- Q14.4(e): Which of the following functions of time represent (a) simple harmonic, (b) periodic but not simple harmonic, and (c) non-periodic motion? Give period for each case of periodic motion ($\omega$ is any positive constant): (e) $exp (–\omega^2t^2)$
- Q14.4(f): Which of the following functions of time represent (a) simple harmonic, (b) periodic but not simple harmonic, and (c) non-periodic motion? Give period for each case of periodic motion ($\omega$ is any positive constant): (f) $1 + \omega t + \omega^2t^2$
- Q14.5(a): A particle is in linear simple harmonic motion between two points, A and B, 10 cm apart. Take the direction from A to B as the positive direction and give the signs of velocity, acceleration and force on the particle when it is (a) at the end A,
- Q14.5(b): A particle is in linear simple harmonic motion between two points, A and B, 10 cm apart. Take the direction from A to B as the positive direction and give the signs of velocity, acceleration and force on the particle when it is (b) at the end B,
- Q14.5(c): A particle is in linear simple harmonic motion between two points, A and B, 10 cm apart. Take the direction from A to B as the positive direction and give the signs of velocity, acceleration and force on the particle when it is (c) at the mid-point of AB going towards A,
- Q14.5(d): A particle is in linear simple harmonic motion between two points, A and B, 10 cm apart. Take the direction from A to B as the positive direction and give the signs of velocity, acceleration and force on the particle when it is (d) at 2 cm away from B going towards A,
- Q14.5(e): A particle is in linear simple harmonic motion between two points, A and B, 10 cm apart. Take the direction from A to B as the positive direction and give the signs of velocity, acceleration and force on the particle when it is (e) at 3 cm away from A going towards B, and
- Q14.5(f): A particle is in linear simple harmonic motion between two points, A and B, 10 cm apart. Take the direction from A to B as the positive direction and give the signs of velocity, acceleration and force on the particle when it is (f) at 4 cm away from B going towards A.
- Q14.6(a): Which of the following relationships between the acceleration $a$ and the displacement $x$ of a particle involve simple harmonic motion? (a) $a = 0.7x$
- Q14.6(b): Which of the following relationships between the acceleration $a$ and the displacement $x$ of a particle involve simple harmonic motion? (b) $a = –200x^2$
- Q14.6(c): Which of the following relationships between the acceleration $a$ and the displacement $x$ of a particle involve simple harmonic motion? (c) $a = –10x$
- Q14.6(d): Which of the following relationships between the acceleration $a$ and the displacement $x$ of a particle involve simple harmonic motion? (d) $a = 100x^3$
- Q14.8: A spring balance has a scale that reads from 0 to 50 kg. The length of the scale is 20 cm. A body suspended from this balance, when displaced and released, oscillates with a period of 0.6 s. What is the weight of the body ?
- Q14.9(i): A spring having with a spring constant $1200 N m^{-1}$ is mounted on a horizontal table as shown in Fig. 14.24. A mass of 3 kg is attached to the free end of the spring. The mass is then pulled sideways to a distance of 2.0 cm and released. Determine (i) the frequency of oscillations,
- Q14.9(ii): A spring having with a spring constant $1200 N m^{-1}$ is mounted on a horizontal table as shown in Fig. 14.24. A mass of 3 kg is attached to the free end of the spring. The mass is then pulled sideways to a distance of 2.0 cm and released. Determine (ii) maximum acceleration of the mass,
- Q14.9(iii): A spring having with a spring constant $1200 N m^{-1}$ is mounted on a horizontal table as shown in Fig. 14.24. A mass of 3 kg is attached to the free end of the spring. The mass is then pulled sideways to a distance of 2.0 cm and released. Determine (iii) the maximum speed of the mass.
CBSE Solutions for Class 11 Physics Oscillations
Chapters in CBSE - Class 11 Physics
Top Tutors who teach Oscillations
(47)
Super Tutor
Panvel, Mumbai
14 yrs of
Exp
30 students
3301 hrs of classes completed
500
per hour
Engineering Graduate, Result Oriented Physics Tutor having more than 15 years of Experience.
Online Classes
I provide private tuition for Physics and Mathematics for Class XI and XII (All Boards) Physics for Engineering Aspirants Physics for Medical Aspirants Class IX and X Mathematics and Science.
Priyadharshini
Devendra sir is really an amazing mentor and a down to heart pearson who is always ready to give you a clear cut idea about the concepts and is an expert in getting the concepts really into my head. With him physics will be made easy and you will not have to struggle at all especially for a student who shifted from 10th to 11th I can tell he is just amazing!!
Skills:
Physics
Also teaches:
NEET-UG Coaching, Class 9 Tuition
and more
(22)
Top Tutor
Sector 61 Block E, Noida
20 yrs of
Exp
2 students
1139 hrs of classes completed
400
per hour
Computer Science for Grades 11 & 12 | Python, C, C++, Java & DSA for B.Tech
Online Classes
Student's Home
Tutor's home
I have extensive teaching experience providing personalized 1:1 Python training to students. My teaching approach focuses on building strong Python fundamentals through interactive lessons, practical examples, and regular coding practice. In 1:1 sessions, I adapt my teaching methods to suit each student's learning pace and individual needs, ensuring concepts are clearly understood. I encourage logical thinking, problem-solving, and hands-on coding, helping students gain confidence, strengthen their Python programming skills, and achieve academic and professional success.
Skills:
Computer Science
Also teaches:
BTech Tuition, Python Training
and more
(11)
Top Tutor
Zafarpur Mahawan, Karari
10 yrs of
Exp
1 student
287 hrs of classes completed
350
per hour
Certified in Finance (from IIM) with over 20 years of experience of teaching in CBSE school
Online Classes
In my school, commerce is introduced in class 11th itself. So it became very significant that students are given all the basic information about their subjects and also to develop keen interest in them by relating the topics to their everyday life. With loads of practice and exemplary notes, the requisite foundation is made. And I make sure the topics are nicely delivered.
Hiba Khaleel
We took online mode from outside india, All classes held on time with excellent explanation and clear communication. Positive recommendations from my side.
Skills:
Accountancy
,
Business Studies
Also teaches:
Spoken English, BCom Tuition
and more
(72)
Top Tutor
Ramanthapur, Hyderabad
20 yrs of
Exp
15 students
100 hrs of classes completed
500
per hour
Accounts Teacher with 27 years of teaching experience
Online Classes
Student's Home
Tutor's home
I have 29 years of teaching experience in college and tuition. I teach students with complete concept and clear all the doubts until students satisfy. I teach in such a manner that students feel comfortable and confident and make students subject very easy and convenient to understand and solve Accounts with full confidence.
Ashish Jha
Dr. Apparao is an awesome accounts experienced reached. Within a month of joining his tuition, my son got confidence and good marks in accountancy. His articulative way of explaining the concepts along with his hold on the subject is outstanding. I would highly recommend him to be opted as teacher of the choice for other students struggling with accounts.
Also teaches:
MBA Tuition, BBA Tuition
and more
(70)
Super Tutor
Nerul, Mumbai
10 yrs of
Exp
6 students
712 hrs of classes completed
800
per hour
Maths Tutor
Online Classes
I'm an ex-faculty member of Allen, FIITJEE & Unacademy, and I taught in DAV for 2 years. Now I'm working as a freelancer. I have more than 10 years of experience. So overall I've all kinds of experience to meet with academic & JEE aspirants as well. Join me to learn mathematics from basic to advanced.
Harsah
Sir, explains topics very clearly nicely explains doubt very nicely with high conceptual knowledge.
Skills:
Mathematics
,
Applied Mathematics
Also teaches:
Class 12 Tuition, Engineering Entrance Coaching
and more
×
